A variable capacitor formed of a thin-film capacitor has a capacitance thereof changeable according to an applied voltage. Such a variable capacitor is expected to be used in a microwave phase shifter, a phased array antenna, a on-vehicle radar device, etc.
For a thin-film or thick-film capacitor that utilizes a metal oxide thin film having a perovskite structure and capable of manifesting a first-order or second-order phase transition, the Landau-Ginzburg-Devonshire theory teaches that electric field E applied to the metal oxide thin film and electric displacement D are related as follows by use of coefficients “a” and “b” (see Non-Patent Document 2).E=aD+bD3  (1)According to the Landau-Ginzburg-Devonshire theory, the coefficient “a” is a first-order function of a temperature while the coefficient “b” has no or little temperature dependency.
By use of ε=dD/dE, a relative permittivity ε of the metal oxide film is expressed as follows.ε=1/(a+3bD2)  (2)
FIG. 1 illustrates a thin-film or thick-film capacitor including a metal oxide film 1 having a perovskite structure of a thickness d and electrodes 2 and 3 of an area size A such that the metal oxide film 1 is placed between the electrodes 2 and 3. For such a capacitor, above-noted formula (2) is modified by use of an electric charge Q and an externally applied voltage V as follows.V=(ad/A)Q+(bd/A3)Q3  (3)
By use of formula (3), a capacitance C is expressed as follows.C=dQ/dV=1/(ad/A+(3bd/A3)Q2)  (4)
Formula (4) indicates that the capacitance C can be changed as depicted in FIG. 2, for example, in response to a voltage change in the case of a thin-or-thick-film capacitor illustrated in FIG. 1.
FIG. 2 illustrates a capacitance-voltage characteristic curve for a thin-film capacitor in which BST (BaSrTiO3) with a film thickness of 80 nm is used as the metal oxide film 1 and Pt is used as the electrodes 2 and 3.
As can be seen from FIG. 2, the capacitance C becomes the maximum around a point where the externally applied voltage V is 0 V. Further, the capacitance C decreases as the externally applied voltage V is changed from 0 V in either a positive direction or a negative direction.
A careful review of the characteristic curve illustrated in FIG. 2 reveals that the slope of the characteristic curve becomes gentle around the peak of the characteristic curve, i.e., around a point where the voltage V is zero volt. The orientation of the characteristic curve becomes horizontal at the point at which the voltage V is zero volt.
Accordingly, the related-art variable capacitor as illustrated in FIG. 2 has a small capacitance change when the capacitor is of a small size with a small drive voltage. It is thus difficult to provide a desired characteristic change for a filter circuit or the like.    [Patent Document 1] Japanese Patent Application Publication No. 10-93050    [Non-Patent Document 1] Qu, B., et al. J. Phys., Condens. Matter 6 1207-1212, Feb. 7, 1994    [Non-Patent Document 2] Taganstev. A. K., et al., J. Electroceramics, 11, 5-66, 2003